Various proposals have been made in the past to meet these requirements and in this connection attention is particularly directed to the Assignee's U.S. prior patent No. 3,894,322 and European patent specification No. 82300954.3. In both cases the insert is held between jaws formed integrally with the tool holder but whilst in the former case the jaws are screw biased into clamping the insert, in the latter case a wedge shaped insert is frictionally held within a wedge shaped slot defined between the jaws. The continguous surfaces of the slot and the insert are formed with elongated keying arrangements so as to inhibit transverse movement of the insert retained within the slot in a direction transverse thereto. The European patent specification furthermore discloses the provision of the insert with an abutment shoulder which limits the degree of insertion of the insert into the holder. Whilst such hitherto proposed systems are in general effective in retaining the insert in its cutting position under the normal inwardly and laterally directing forces which act on the insert during cutting, it has been found that outward displacement of the insert may take place when traction forces are exerted thereon. Such traction forces may arise in the course of various cutting operations such as, for example, during the internal chamfering of a pipe edge.